Kramers pseudospin and the quantum number proposed for the many-electron Dirac?Coulomb Hamiltonian

Title:Kramers pseudospin and the quantum number proposed for the many-electron Dirac?Coulomb Hamiltonian

Abstract:The square of a sum of single-electron time reversals has been proposed as a conserved quantity with an integer eigenvalue spectrum for the many-electron Dirac-Coulomb Hamiltonian [Phys. Rev. A 94, 052104 (2016)], and its expectation value is in use as a diagnostic of Kramers contamination. This work identifies the operator behind the construction, a component of a pseudospin attached to the chosen Kramers pairs, whose angular-momentum algebra reproduces the reported spectrum and yields the eigenvectors in closed form. The label $k$ entering the proposed quantum number $-k^2$ is twice the magnitude of a pseudospin projection onto an axis fixed by the basis and changes when the Kramers pairs are rephased. The commutation with the Hamiltonian is unfounded, and the proposed quantum number does not stand.

Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)

arXiv:2608.27112 [quant-ph]

(or arXiv:2608.27112v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.27112 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.